What helped me advance when I was at the same point and striving for the simple goals was to set a fixed number of deep breaths between the sets of the swings as my prescribed rest period. I saw this idea somewhere on here, can't remember who, think it was an adaptation of Iron Tamer's breathing ladders into S&S.
I started somewhere around 5. Do the nasal breathing as has been described many places on here and breath deep into the gut. You will be surprised at how much rest you will actually get with 5 deep breaths.
Even starting with 5, towards the end of the swings you may get that panicked feeling in your lungs when your mind is telling you that you aren't getting enough air and absolutely have to breath faster, but you will see in time that you don't. Once you feel comfortable at a fixed number of breaths between sets, decrease to 4 breaths between sets...stay there until comfortable, then decrease again. Keep doing this until you are in the 2-3 breath range and then try timing yourself again, you should be quite close at that point.
Anyways, that's what helped me, hope it can help you too.
